Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

COARSE MESH FINITE DIFFERENCE ACCELERATION OF DISCRETE ORDINATE NEUTRON TRANSPORT CALCULATION EMPLOYING DISCONTINUOUS FINITE ELEMENT METHOD

  • Lee, Dong Wook (Department of Nuclear Engineering, Seoul National University) ;
  • Joo, Han Gyu (Department of Nuclear Engineering, Seoul National University)
  • Received : 2014.06.10
  • Accepted : 2014.07.29
  • Published : 2014.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

The coarse mesh finite difference (CMFD) method is applied to the discontinuous finite element method based discrete ordinate calculation for source convergence acceleration. The three-dimensional (3-D) DFEM-Sn code FEDONA is developed for general geometry applications as a framework for the CMFD implementation. Detailed methods for applying the CMFD acceleration are established, such as the method to acquire the coarse mesh flux and current by combining unstructured tetrahedron elements to rectangular coarse mesh geometry, and the alternating calculation method to exchange the updated flux information between the CMFD and DFEM-Sn. The partial current based CMFD (p-CMFD) is also implemented for comparison of the acceleration performance. The modified p-CMFD method is proposed to correct the weakness of the original p-CMFD formulation. The performance of CMFD acceleration is examined first for simple two-dimensional multigroup problems to investigate the effect of the problem and coarse mesh sizes. It is shown that smaller coarse meshes are more effective in the CMFD acceleration and the modified p-CMFD has similar effectiveness as the standard CMFD. The effectiveness of CMFD acceleration is then assessed for three-dimensional benchmark problems such as the IAEA (International Atomic Energy Agency) and C5G7MOX problems. It is demonstrated that a sufficiently converged solution is obtained within 7 outer iterations which would require 175 iterations with the normal DFEM-Sn calculations for the IAEA problem. It is claimed that the CMFD accelerated DFEM-Sn method can be effectively used in the practical eigenvalue calculations involving general geometries.

Keywords

References

  1. T .A. Wareing et al., "Discontinuous Finite Element SN Methods on Three-Dimensional Unstructured Grids," Nucl. Sci. Eng., 138, 256-268 (2001). https://doi.org/10.13182/NSE138-256
  2. J . M. McGhee, T.A. Wareing and D.A. Barnett Jr., ATTILA User's Manual, Transpire, Inc. (2007).
  3. S .G. Hong et al., "Development of MUST (Multi-group Unstructured geometry Sn Transport) Code," Trans. of the Korean Nuclear Society, Gyeongju, Korea (2009).
  4. W .H. Reed and T.R. Hill, Triangular Mesh Methods for the Neutron Transport Equation, Los Alamos Scientific Laboratory Report, LA-UR-83-479 (1973).
  5. B . Cockburn et al., "Discontinuous Galerkin Methods: Theory Computation and Applications," Lecture Notes in Computational Science and Engineering, Vol. 11, Springer-Verlag, New York, USA (2000).
  6. K .S. Smith, "Nodal method storage reduction by non-linear iteration," Trans. of the American Nuclear Society, 44, 265 (1983).
  7. K .S. Smith and J.D. Rhodes III, "Full-core, 2-D, LWR core calculations with CASMO-4E," Proc. of the ANS Reactor Physics Topical Meeting, Seoul, Korea (2002).
  8. J .Y. Cho et al., "Cell based CMFD formulation for acceleration of whole-core method of characteristics calculation," J. of the Korean Nuclear Society, 34, 250-258 (2002).
  9. Z . Zhong, T.J. Downar and Y. Xu, "Implementation of Two-Level Coarse-Mesh Finite Difference Acceleration in an Arbitrary Geometry, Two-Dimensional Discrete Ordinates Transport Method," Nucl. Sci. Eng, 158, 289-298 (2008). https://doi.org/10.13182/NSE06-24TN
  10. K.S. Kim, M.D. DeHart, "Unstructured partial- and netcurrent based coarse mesh finite difference acceleration applied to the extended step characteristics method in NEWT," Annals of Nuclear Energy, 38, 527-534 (2011). https://doi.org/10.1016/j.anucene.2010.09.011
  11. M.J. Lee, H. G. Joo, D. J. Lee and K. Smith, "Coarse mesh finite difference formulation for accelerated Monte Carlo eigenvalue calculation," Annals of Nuclear Energy, 65, 101-113 (2014). https://doi.org/10.1016/j.anucene.2013.10.025
  12. H.G. Joo et al., "Dynamic implementation of the equivalence theory in the heterogeneous whole core transport calculation," Proc of the ANS Reactor Physics Topical Meeting, Seoul, Korea (2002).
  13. R.E. Alcouffe, "The Diffusion Synthetic Acceleration Methods for the Diamond-Differenced Discrete-Ordinates Equations," Nucl. Sci. Eng., 64, 344 (1997).
  14. E.W. Larsen, "Unconditionally Stable Diffusion Synthetic Acceleration Methods for the Slab Geometry Discrete Ordinates Equations. Part I: Theory," Nucl. Sci. Eng., 82, 47 (1982). https://doi.org/10.13182/NSE82-1
  15. M.L. Adams and W.R. Martin, "Diffusion Synthetic Acceleration of Discontinuous Finite Element Transport Iterations," Nucl. Sci. Eng., 111, 145 (1992). https://doi.org/10.13182/NSE92-A23930
  16. J.S. Warsa, T.A. Wareing and J.E. Morel, "Fully consistent diffusion synthetic acceleration of linear discontinuous SN transport discretizations on unstructured tetrahedral meshes," Nucl. Sci. Eng., 141, no.3, 236-251 (2002). https://doi.org/10.13182/NSE141-236
  17. J.S. Warsa, T.A. Wareing and J.E. Morel, "On the degraded effectiveness of diffusion synthetic acceleration for multidimensional Sn calculations in the presence of material discontinuities," Proc. of Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Gatlinburg, TN, USA (2003).
  18. N.Z. Cho et al., "On a new acceleration method for 3D whole core transport calculations," Proc. Annual Meeting of Atomic Energy Society of Japan, Sasebo, Japan (2003).
  19. C. Geuzaine and J.F. Remacle, "Gmsh: a three dimensional finite element mesh generator with built-in pre and post processing facilities," Int. Journal for Numerical Methods in Engineering, 79, Issue 11, 1309 (2009). https://doi.org/10.1002/nme.2579
  20. N.Z. Cho and C.J. Park, "A Comparison of Coarse Mesh Rebalance and Coarse Mesh Finite Difference Accelerations for the Neutron Transport Calculations," Proc. of Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Gatlinburg, TN, USA (2003).
  21. A. Yamamoto et al., "Convergence Improvement of Coarse Mesh Rebalance Method for Neutron Transport Calculations," J. of Nucl. Sci. Technol., 41, 781-789 (2004). https://doi.org/10.1080/18811248.2004.9715547
  22. S.G. Hong, K.S. Kim and J.S. Song, "Fourier Convergence Analysis of the Rebalance Methods for Discrete Ordinates Transport Equations in Eigenvalue Problems," Nucl. Sci. Eng., 164, 33-52 (2010). https://doi.org/10.13182/NSE09-18
  23. E. Lewis et al., Benchmark Specification for Deterministic 2-D/3-D MOX fuel Assembly Transport Calculations without Spatial Homogenization (C5G7MOX), NEA/NSC/DOC 4 (2001).
  24. Argonne Code Center, Benchmark Problem Book, Report ANL-7416 (Suppl. 2). Argonne National Laboratory, Argonne, IL (1977).
  25. LLNL, VisIt User's Manual, Lawrence Livermore National Laboratory Report, UCRL-SM-220449 (2005).
  26. H.G. Joo and T.J. Downar, "An incomplete domain decom-position preconditioning method for nonlinear nodal kinetics calculations," Nucl. Sci. Eng., 123, 403-414 (1996). https://doi.org/10.13182/NSE96-A24203

Cited by

  1. Quantitative Fissile Assay In Used Fuel Using LSDS System vol.153, pp.2100-014X, 2017, https://doi.org/10.1051/epjconf/201715305010